# Graphing Horizontal Lines

Horizontal lines have **zero slope.** To graph a horizontal line in the standard coordinate system, use the equation $y = k ,$ where $k$ gives the point on the $y$-axis that the line will intersect.

## The Slope of a Horizontal Line

## Why We Use $y=k$

Suppose we want a horizontal line that passes through $(0,5) .$

In addition to that point, the line will pass through

$\ldots, (-3, 5), (-2, 5), (-1, 5), (1, 5), (2, 5), (3, 5), \ldots$

and in general for any real number $Q,$ the graph will pass through $(Q, 5) .$

This means the $x$-coordinate can vary to any real number, so it doesn't get fixed at all and doesn't need to appear in the horizontal line equation. $y$ on the other hand must always be 5, giving an equation of $y = 5 .$

Note that if we attempt to use a traditional line form, like the slope-intercept form $y = mx + b ,$ we create a line with the equation $y=0x+b,$ or $y=b,$ where $b$ is the $y$-intercept of the line.

## What is the equation of the line that passes through the points $(5, 4)$ and $(-2,4)\,?$

Because both of the points on the line have a $y$-value of 4, every point on the line will have a $y$-value of 4 and the equation of the horizontal line is $y=4.$

**Cite as:**Graphing Horizontal Lines.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/graphing-horizontal-lines/